The simple answer is YES... even if a company claims they won't due to their purity, BUT, here is what you need to know...
Essential oils shouldn't go rancid, unless they are mixed with carrier oils or other synthetic or adulterated substances. However, they can oxidize. Three things come into play with oxidation: light, heat, and oxygen.
Oxidation is a process in which a chemical substance changes due to heat, light, and oxygen. What happens is that it is going to change or degrade the composition of the oil. Citrus oils are high in d-limonene, what will happen is that after the bottle is open, it will begin to oxidize over time meaning that the d-limonene levels will go down. You may not notice this as it will smell the same, but the therapeutics can decrease, and the risk for a dermal reaction may occur. Citrus oils can become cloudy if oxidized.
Some oils, especially citrus oils should actually be stored in the refrigerator to prevent oxidation to protect them from heat exposure.
Most essential oils come in dark amber or blue bottles, which helps to protect them from light, but once we use them in homemade products they will be exposed to light and oxidation can occur. Most oils last between 2-3 years, some more, some less.
When you are using your oils and you have oxygen in the bottles is that you can transfer them to smaller bottles. You can also date the bottles with the month and year of when you opened the bottle. Unopened bottles will be fine as long as they are stored properly.
When it comes to light exposure, you want to avoid direct contact with sunlight. May of us keep our oils on display, but there are things that can be done to avoid sun exposure. I keep my oils in a case that has foam enclosures in which the oils sit.
If your oils become oxidized, it is recommended to not diffuse them or use them dermally, but you can use them in your cleaning products without any issues.
The oils most prone to oxidation are: Angelica Root, Bergamot Mint, Cannabis, Cilantro, Elemi, Grapefruit, Lemon, Lime, Mandarin, Manuka, Melissa, Neroli, Orange (all types), Palo Santo, Rhododendron, Taget, Tangerine, and Yuzu. [Source: The Tisserand Institute]
